First Problem of Stokes for Generalized Burgers' Fluids. (4th March 2012)

• Record Type: Journal Article
• Authors: Jamil, Muhammad
• Other Names: Radinschi I. Academic Editor.; Steeb W.-H. Academic Editor.
• Is Part Of: ISRN mathematical physics. Volume 2012(2012)
• Publication Date: 2012-03-04
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Electronic journals; Periodicals; 530.15
• DOI: 10.5402/2012/831063
• Languages: English
• ISSNs: 2090-4673

Abstract

Abstract : The velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers' fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.